Igneous Rocks are classified is several ways, and methods of classification have evolved a lot over the past 100 years. Each classification is useful for a certain purpose and reflect a particular way of looking at igneous rocks.
All rock classifications are based on two criteria, however, mineral content of the rock, and texture (grain size). A complete classification must include both components, although with igneous rocks both components are usually built into one rock name, for example, granite is a light colored/coarse grained rock. (This is unlike sedimentary rocks where a name like "arkosic sandstone"specifies both components separately; arkose meaning lots of feldspar and sandstone being the texture.)
Here we examine three classifications beginning with the simplest and easiest to use (but also the most inaccurate) and proceeding to more useful, but more complex, classifictions:

It is not at all clear why, but minerals at the top of Bowen's Reaction Series tend to be dark in color (e.g. pyroxene and amphibole), and minerals at the bottom tend to be light in color (e.g. Na plagioclase and quartz). After all, what could temperature of formation have to do with mineral color?
And it is also not clear why, but magma compositions tend to segregate out, mafic magmas at the top of Bowen's Reaction Series, intermediate magmas in the middle, and felsic at the bottom. Result? Mafic magmas produce dark colored rocks made of dark minerals (such as basalt), intermediate magmas intermediate colored rocks (e.g. diorite) and felsic magmas light colored rocks (e.g. granite).
Because of these fortuitous conditions it is natural to classifiy igneous rock on color and texture. As a first approximation, a classification based on color and texture is ok, but can lead to great mistakes and ultimately a color/texture classification is inadequate. Thus, other classifications exist, per below.

A modal classification includes the common names like granite, basalt, diorite, etc. The classification is based on arbitrarily defined boundaries between classes on a ternary diagram. In general the modal names correspond with names derived from a color/texture classification, it is just the decision on what to call a rock is based on mineral content rather than color. Such a classification works readily in a key. Go to Composition/Texture Key (not "clickable" yet) - pdf version (clickable)

But the classification is also commonly displayed as a "Mineral Percent Abundance" chart. Go to Mineral Percent Abundance Chart (completely clickable with lots of pictures.)

Observe that to identify rocks in this classification it is necessary to make several crucial observations and decisions. The first is how much quartz does the rock have; >20% and the specimen can be only one of three rocks, alkaligranite, plagiogranite, or granodiorite (see key).
A second decision is whether the rock is dominated by feldspars (see key).
A third decision is whether the rock is about a 50/50 mixture of mafics and feldspar (see key).
And finally a decision on whether the rock is mostly mafics see key).

These decisions divide the rocks into four broad categories which are then easier to remember. It is definitely better to have a systematic strategy for observing and idenifying the rocks than just going at it randomly.

SUITESA Normative Igneous Classification

The normative classification groups together igneous rocks we normally think of as unrelated, such as basalt, diorite, and granite. For this reason normative rock classification is not as easy as in a color/texture or composition/texture system. These rocks do have different mineral assemblages, but may be very similar in their chemistry, reflecting an origin from a common parent magma via fractionation.
On the other hand, a normative classification works extraordinarily well when igneous rocks are examined in terms of plate tectonic processes, the place we ultimately want to go. It is the level at which geologists must study igneous rocks. In compensation, however, for those not interestd in the details, it is possible for a normative classification to in fact be simpler to use when discussing how the earth works.
The normative classification arranges igneous rocks into suites, each suite characterized by a particular chemistry. The four major suites are summarized in a table along with descriptions of each. The are the komatiite, tholeiitic, calcalkaline, and alkaline. Once we become familiar with these it is possible to talk about earth history in terms of the four suites alone, and largely avoid reference to specific rocks.
So, from here we can examine suites from a couple of different perspectives.Suite ChemistrySuite FractionationSuite Tectonic Distribution

Suite Chemistry:
Suites are characterized by three chemical signatures: silica saturation, iron enrichment, and the alkali index, each discussed below and summarized in the table link.Silica saturation is a measure of the amount of SiO2 available in a magma or rock. Silica under saturation is when SiO2 is low enough there is not only not enough to form quartz, there is insufficient to form other minerals such as feldspars. The result is silica poor feldspathoid minerals, such as nephaline and sodalite. Over saturation is when enough SiO2 exists for quartz to crystallize out. If SiO2 is high enough it is possible to have a basalt with quartz, an association not commonly thought to exist. (Go to table link.)
The alkali index measures the amount of Ca (calcium) from the top of Bowen's Reactiion Series (BRS) relative to the amount of Na+K (sodium+potassium) from the bottom of BRS. Alkali indexes greater than 1 indicate high Ca content typical of the top of..BRS. Indexes less than 1 indicate low Ca and high Na+K typical of the bottom of BRS. (Go to table link.)
Since in the fractionation process elements low in the reaction series are "sweated" out first we expect the first fractionated melts to be higher in Na+K than the unmelted residue. Since the tholeiitic, calcalkaline, and alkaline suites have alkali indexes (>1) (1) (<1), they form a fractionation sequence (see below).Iron enrichment declines steadily with fractionation. This is a measure of the decrease in the importance of ferromagnesium minerals down the reaction series. Iron is low in the Komatiite suite because the ultramafic components Mg, Ni, and Cr are so high. (Go to table link.)

Suite Fractionation:
Igneous rock evolution can occur both within and among the suites.
Within suite evolution occurs when, for example, a calcalkaline suite evolves from a diorite to a granite, or a komatiite suite evolves from a peridotite to a basalt to an andesite.
Among suite evolution occurs in volcanic arcs, and other places, when the first igneous activity begins silica over saturated with alkali indexes >1, and evolves to silica under saturated with alkali indexes <1. That is, tholeiitic, followed by calcalkaline, and finally alkaline suites. Cross section.Another evolutionary process occurs when one fractionated igneous rock is re-fractionated at a later time. This would occur, for example, if a fractionated diorite magma emplaced and solidified into a batholith. If this batholith is later heated, a second, more felsic, fractional product (granite) could be sweated out of it, leaving behind a more mafic residue. Also, a rock of one suite may re-fractionate to a melt with the characteristics of another suite.

Suite Tectonic Association:
One important feature of the suites is their association with particular tectonic regimes (go to table). This knowledge is valuable in understanding and reconstructing ancient tectonic events when most of the evidence is destroyed or otherwise unavailable. By analyzing the chemistry of the rocks we can reconstruct the processes by which they formed.
The cross section shows typical tectonic conditions under which each suite forms. A divergent plate boundary (rift) is on the right and a subduction on the left. The large arrows rising on the right, pointing horizontally across the middle, and descending into the subduction zone on the left marks the path the igneous rocks take. From step to step the evolutionary processes described above occur in sequence.
Fractionation takes place in two primary tectonic regimes. First is at rifting centers. Silica over saturated parent rocks (komatiites in the Archean, other ultramafics since then) rise to the surface and fractionally melt. The melt is tholeiitic and rises to the surface to form the pillow basalts and sheeted dikes of ocean crust. The unmelted residue is usually silica under saturated ultramafics which stay in the mantle as layer 4 in the ophiolite suite. (Note that the ophiolite "suite" is NOT a suite in the same sense as calcalkaline, etc. suites.
The second fractionation takes place at convergent boundaries. The tholeiitic oceanic crust moves away from the rifting center until it is subducted. It heats up during subduction and fractionally melts. Typically the first melts erupting closest to the trench are still tholeiitic, but in time the melts evolve to the calcalkaline suite, which build most of the volcanic arc. Later melts become alkaline. These may come from the secondary fractionation of a melt or rock of the calcalkaline suite.
The residue of the fractionation occurring along the subduction zone is ultramafic (peridotite) and continues to descend into the mantle, where it is permanently stored.

Fractionation is Irreversible
Note that the sequence of fractionations is a one way path. This is because the original parent rock begins silica over saturated, but at each fractionation silica and elements low in the reaction series are sweated off. At the end the only thing remaining is the most sterile, ultramafic residue, rich in Mg, Cr, and Ni, and poor in silica and alkali elements. There is nothing remaining to fractionate off.

Conclusions

The present day earth is the result of an evolutionary rock cycle. The earth began as a planet with a limited variety of rock types and has evolved to a state where a very large variety of rocks exist. Furthermore, no mechanisms exist to reverse the processes. The earth cannot devolve to something simpler.
In another sense the earth is behaving as a dissipative structure. All the tectonic and igneous processes require energy, and the dissipation of that energy has resulted in an earth which has gone from a simple composition, and evolved to greater and greater complexity measured by the increasing variety of rocks composing the earth.